Exploring the Minimum Possible Energy: A Question on Energy

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In summary, the concept of a minimum amount of energy is subjective and depends on the context. While there may not be a general minimum energy, every type of energy has a minimum in a specific situation. Energy can be quantized in systems with bound states, but not in free particles. The two models of reality, Classical Mechanics and Quantum Mechanics, have different understandings of energy and whether it is continuous or discrete. In Quantum Mechanics, energy can be either quantized or continuous depending on the system.
  • #1
Icebreaker
Is there an amount of energy than which there is no lower? That is, the minimum amount of energy possible.
 
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  • #2
The zero of most forms of energy is an arbitrary choice, so the answer is "no". There is no minimum to energy in general.

On the other hand, every type of energy has a minimum in a particular situation. For example, the kinetic energy of an object is related to its speed. Since the speed can never be less than zero, the lowest kinetic energy an object can have is zero.
 
  • #3
Oops, I meant to ask minimum non-zero energy. An amount of energy that simply can not be subdivided.
 
  • #4
Icebreaker said:
Oops, I meant to ask minimum non-zero energy. An amount of energy that simply can not be subdivided.

Energy is quantised in any system where there is a bound state. That quantum of energy is indeed the minimum.
 
  • #5
Please clarify "bound state". Are there instances where energy is not quantized?
 
  • #6
An elemtary example of energy quantization is in the H atom, where the lowest possible (ground state) energy of the electron is about -13.6 eV (minimum 13.6 eV is needed to free it from the H atom when it's in this state). And as long as the electron is attached to the H atom, it can only have certain discrete values of energy, [tex]E_n = \frac{-13.6 \mbox{eV}}{n^2}[/tex], where n is called the energy level and can be any integer greater than or equal to 1.

A free particle on the other hand (for example an electron that isn't attached to a nucleus), can have any positive energy (E is a continuous spectrum), as far as I know.
 
  • #7
You can also have bands of continuous energy states separated by an energy gap. Semiconductors and band insulators are such examples.

Zz.
 
  • #8
So the kinetic energy of some matter is continuous?
 
  • #9
Icebreaker said:
So the kinetic energy of some matter is continuous?

Which model of reality are you talking about? We have two very successful ones.

In the one called "Classical Mechanics" the kinetic energy of a body is continuous and is given by
[tex]\frac{1}{2}m|\dot{x}+\dot{y}+\dot{z}|[/tex]

In the other one (which has a greater domain of applicability) called "Quantum Mechanics" the classical concept of energy we can extract from some physical situation can be either quantised, which means it's not continuous, or continuous depending on how the system is set up. We usually determine the states and their corresponding energies by solving the following equation:
[tex]\hat{H}|\psi\rangle=E|\psi\rangle[/tex]

If you do not understand the symbols/ideas involved I suggest you read a book on the subject.
 

FAQ: Exploring the Minimum Possible Energy: A Question on Energy

What is the concept of minimum possible energy?

The minimum possible energy refers to the lowest amount of energy that a system or object can possess. It is a fundamental concept in physics and is often associated with the laws of thermodynamics.

Why is exploring the minimum possible energy important?

Exploring the minimum possible energy allows us to understand the fundamental laws and principles that govern the behavior of energy in our universe. It also has practical applications in fields such as engineering, chemistry, and biology.

How do scientists determine the minimum possible energy of a system?

Scientists use various mathematical and computational methods to determine the minimum possible energy of a system. This can involve solving equations, performing simulations, and using experimental data.

What are some examples of systems with minimum possible energy?

Some examples of systems with minimum possible energy include atoms and molecules in their ground state, a pendulum at its lowest point, and a ball rolling to the bottom of a hill without any external forces acting on it.

Can the minimum possible energy be reached or exceeded?

In theory, the minimum possible energy can be reached but not exceeded. This is because of the laws of thermodynamics, which state that energy cannot be created or destroyed, only converted from one form to another. However, in practice, it may be difficult or impossible to reach the absolute minimum possible energy due to various factors such as external influences and imperfections in the system.

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